Peer-review (also known as refereeing) is the process journal editors use to ensure the articles they publish meet the standards of good scholarship. Academic papers (journal articles, research papers, etc) are examined by a panel of other scholars in the field (the author's peers). The panel may decide to accept the paper, recommend revision or reject it completely. Any resource that passes the peer-review process can be considered to have the highest level of academic credibility - although of course you still need to consider other elements such as age and relevance.
Many of your assignments will specify that only peer-reviewed resources are to be used. This means you will need to evaluate the journal articles you find as many journals don't peer-review their papers.